Anharmonicity, vibrational instability and Boson peak in glasses

Details Anharmonicity, vibrational instability and Boson peak in glasses Anharmonicity, vibrational instability and Boson peak in glasses

2002-03-07

arxiv.org/abs/cond-mat/0203165v2

Phys. Rev. B 67, 094203 (2003)

Physics

Condensed Matter

Disordered Systems and Neural Networks

LaTeX, 8 pages, 6 figures

Scientific paper

10.1103/PhysRevB.67.094203

We show that a {\em vibrational instability} of the spectrum of weakly interacting quasi-local harmonic modes creates the maximum in the inelastic scattering intensity in glasses, the Boson peak. The instability, limited by anharmonicity, causes a complete reconstruction of the vibrational density of states (DOS) below some frequency $\omega_c$, proportional to the strength of interaction. The DOS of the new {\em harmonic modes} is independent of the actual value of the anharmonicity. It is a universal function of frequency depending on a single parameter -- the Boson peak frequency, $\omega_b$ which is a function of interaction strength. The excess of the DOS over the Debye value is $\propto\omega^4$ at low frequencies and linear in $\omega$ in the interval $\omega_b \ll \omega \ll \omega_c$. Our results are in an excellent agreement with recent experimental studies.

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